Problem: Let $h(x)=x^2-7x+2$. $h'(x)=$
According to the sum rule, the derivative of $x^2-7x+2$ is the sum of the derivatives of $x^2$, $-7x$, and $2$. The derivatives of these terms can be found using the power rule : $\dfrac{d}{dx}(x^n)=n\cdot x^{n-1}$ For example, this is the derivative of the first term: $\dfrac{d}{dx}(x^2)=2x$ Here is the complete differentiation process: $\begin{aligned} &\phantom{=}h'(x) \\\\ &=\dfrac{d}{dx}(x^2-7x+2) \\\\ &=\dfrac{d}{dx}(x^2)-7\dfrac{d}{dx}(x)+\dfrac{d}{dx}(2)&&\gray{\text{Basic differentiation rules}} \\\\ &=\dfrac{d}{dx}(x^2)-7\dfrac{d}{dx}(x)+0&&\gray{\text{Constant Rule}} \\\\ &=2x-7\cdot 1x^0&&\gray{\text{The power rule}} \\\\ &=2x-7 \end{aligned}$ In conclusion, $h'(x)=2x-7$.